Method for determining the correlation between a received beacon signal and a reconstructed signal

ABSTRACT

The invention relates to a method for determining the correlation between a signal transmitted by a beacon and tracked by a receiver and a reconstructed signal expected to be received at the receiver, wherein the received signal and the reconstructed signal are shifted against each other. In order to provide a possibility of compensating residual sinusoidal modulations in the tracked signal, it is proposed that at each shifting position, the samples of the received and the reconstructed signal are multiplied and integrated separately in a plurality of sections. The results are multiplied with a shifted and complex conjugated version of itself. The products resulting in this second multiplication are integrated to receive a single final value for each shifting position. Finally, the maximum final value resulting for the different shifting positions is determined, the shifting position with the maximum value being considered as the shifting position with the maximum correlation.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 USC §119 to InternationalPatent Application No. PCT/IB02/00982 having an international filingdate of Mar. 28, 2002.

FIELD OF THE INVENTION

The invention relates to a method for determining the correlationbetween on the one hand a signal transmitted by a beacon and received ata receiver tracking said beacon and on the other hand a reconstructedsignal expected to be received at said receiver from said beacon. Fordetermining the correlation, the received signal and the reconstructedsignal are shifted against each other. The invention relates inparticular to a determination of the correlation for the case that thereceived signal comprises undesired sinusoidal modulations. Theinvention relates equally to a corresponding receiver and to apositioning system comprising a receiver.

BACKGROUND OF THE INVENTION

A well known positioning system which is based on the evaluation ofsignals transmitted by beacons is GPS (Global Positioning System). Theconstellation in GPS consists of more than 20 satellites employed asbeacons that orbit the earth. The distribution of these satellitesensure that usually between five and eight satellites are visible fromany point on the earth.

Each of the satellites, which are also called space vehicles (SV),transmits two microwave carrier signals. One of these carrier signals L1is employed for carrying a navigation message and code signals of astandard positioning service (SPS). The L1 carrier phase is modulated byeach satellite with a different C/A (Coarse Acquisition) Code. Thus,different channels are obtained for the transmission by the differentsatellites. The C/A code, which is spreading the spectrum over a 1 MHzbandwidth, is repeated every 1023 bits, the epoch of the code being 1ms. The carrier frequency of the L1 signal is further modulated withnavigation information at a bit rate of 50 bit/s, which informationcomprises in particular ephemeris and almanac data. Ephemeris parametersdescribe short sections of the orbit of the respective satellite. Basedon these ephemeris parameters, an algorithm can estimate the position ofthe satellite for any time while the satellite is in the respectivedescribed section. The orbits calculated using ephemeris parameters arequite accurate, but the ephemeris parameters are only valid for a shorttime, i.e. for about 2-4 hours. The almanac data, in contrast, containcoarse orbit parameters. The orbits calculated based on almanac data arenot as accurate as the orbits calculated based on ephemeris data, butthey are valid for more than one week. Almanac and ephemeris data alsocomprise clock correction parameters which indicate the currentdeviation of the satellite clock versus a general GPS time.

Further, a time-of-week TOW count is reported every six seconds asanother part of the navigation message.

A GPS receiver of which the position is to be determined receives thesignals transmitted by the currently available satellites, and atracking unit of the receiver detects and tracks the channels used bydifferent satellites based on the different comprised C/A codes. Thereceiver first determines the time of transmission of the codetransmitted by each satellite. Usually, the estimated time oftransmission is composed of two components. A first component is the TOWcount extracted from the decoded navigation message in the signals fromthe satellite, which has a precision of six seconds. A second componentis based on counting the epochs and chips from the time at which thebits indicating the TOW are received in the tracking unit of thereceiver. The epoch and chip count provides the receiver with themilliseconds and sub-milliseconds of the time of transmission ofspecific received bits.

Based on the time of transmission and the measured time of arrival TOAof the signal at the receiver, the time of flight TOF required by thesignal to propagate from the satellite to the receiver is determined. Bymultiplying this TOF with the speed of light, it is converted to thedistance between the receiver and the respective satellite. The computeddistance between a specific satellite and a receiver is calledpseudo-range, because the general GPS time is not accurately known inthe receiver. Usually, the receiver calculates the accurate time ofarrival of a signal based on some initial estimate, and the moreaccurate the initial time estimate is, the more efficient are positionand accurate time calculations. A reference GPS time can, but does nothave to be provided to the receiver by a network.

The computed distances and the estimated positions of the satellitesthen permit a calculation of the current position of the receiver, sincethe receiver is located at an intersection of the pseudo-ranges from aset of satellites. In order to be able to compute a position of areceiver in three dimensions and the time offset in the receiver clock,the signals from four different GPS satellite signals are required.

If navigation data are available on one of the receiver channels, theindication of the time of transmission comprised in a received signalcan also be used in a time initialization for correcting a clock errorin the receiver. In GPS, an initial time estimate is needed for thepositioning. For the initial time estimate, the average propagation timeof satellite signal of around 0.078 seconds is added to the time oftransmission extracted from the navigation information. The result isused as initial estimate of the time of arrival of a signal, whichestimate lies within around 20 ms of the accurate time of arrival. Thereceiver then determines for different satellites the time at which arespective signal left the satellite. Using the initial estimate of thecurrent time, the receiver forms pseudorange measurements as the timeinterval during which the respective signal was propagating from thesatellite to the receiver either in seconds or in meters by scaling withthe speed of light. After the position of the receiver has beencalculated from the determined pseudoranges, the accurate time ofreception can then be calculated from standard GPS equations with anaccuracy of 1 μs.

However, in order to be able to make use of such a time initialization,the navigation data from a satellite signal is needed. Currently, mostof the GPS receivers are designed for outdoor operations with goodsignal levels from satellites. Thus, only good propagation conditionsensure that the navigation data required for the described timeinitialization is available.

In bad propagation conditions, in contrast, it may not be possible toextract the navigation message accurately enough from received satellitesignals, since a high bit-error rate and weak signal levels make arobust decoding of navigation bits impossible. Such bad propagationconditions, which are often given indoors, render the timeinitialization and the pseudorange measurements more difficult.

For those cases in which the standard time initialization methods cannot be applied since the navigation data are noisy, the timeinitialization process for the receiver can be performed by a timerecovery method. Some known time recovery methods are based on thecross-correlation of the tracked signal and an expected signal to definethe time of transmission, as will be explained in the following.

Even in bad propagation conditions, the receiver might still be able totrack the signal of a GPS satellite and to provide raw data without anevaluation of the contained bit values. Further, some information aboutthe satellites, e.g. ephemeris and/or almanac data, might be obtainedfrom a network, which a-priori knowledge of the GPS signal content wouldenable a reconstruction of certain fragments of the navigation datastream. The reconstructed data could then be utilized for the timeinitialization and position calculations using a cross-correlation basedtechnique.

For the cross-correlation methods, the received raw data and expecteddata are shifted against each other. For each shifting position, apointwise multiplication of the overlapping parts of the two signals isperformed, taking into account different sampling rates. Themultiplications for each shifting position are followed by anintegration of the results. The best match between overlapping parts ofthe expected signal and the received raw data is assumed to be given atthe shifting position resulting in the highest value in the integration.

This best match allows the determination of a time-stamp, i.e. the lastbit edge transmission time, on the received signal, similar to the TOWin the conventional approach. From this time-stamp, the time oftransmission of the tracked signal can then be estimated by countingcorresponding epochs and chips from this time-stamp. The receiver timecan be obtained by adding the average time of flight, or a moreaccurately estimated value of the time of flight, to the estimated timeof transmission. Alternatively, GPS equations can be solved fordetermining the accurate receiver time. This alternative constitutes theconventional method for determining the accurate receiver time, but itrequires an estimated time of transmission of signals from at least foursatellites.

In cross-correlation methods, however, a problem might result fromdistortions in the received signals that are not wiped-off ideally bythe tracking loops. In weak signal conditions, the operating mode of thetracking unit of the receiver is quite unstable, and a severe sinusoidalmodulation may remain in the tracked raw data. Such uncompensatedfrequency distortions can result in particular from Doppler frequencyshifts caused by relative receiver and satellite movements and by aclock inaccuracy.

Even a small remaining Doppler frequency shift is dangerous, since thecross-correlation based time-recovery methods integrate over severalseconds, typically over 1 s to 6 s. Even if a perfect match is achievedduring cross-correlation, the cross-correlation value can be very smalldue to the sinusoidal modulation. This becomes quite evident from thefact that after a correct alignment of the raw data and thereconstructed bits and performing an elementwise multiplication of thesamples in both arrays, the data modulation is wiped-off, while thesinusoidal modulation still remains. In a real environment, the Dopplermodulation is usually quite random, but in the worst case, a fixedmodulation frequency will result. The cross-correlation algorithm willthen integrate the complex sinusoid and output a small value. Thus, thematch between the received raw data and the corresponding fragment ofthe expected signal will not be detected.

In a known approach for compensating sinusoidal modulations, thereceived and the expected signals are both separately multiplied by theshifted complex conjugate copy of the signal itself. Thereafter, thereceived and expected signals are cross-correlated in a conventionalmanner.

SUMMARY OF THE INVENTION

It is an object of the invention to provide a cross-correlation methodwhich compensates for residual sinusoidal modulations, in particularDoppler modulations, in tracked signals of a beacon. It is further anobject of the invention to provide an alternative to the known approachfor compensating for sinusoidal modulations in the tracked signals of abeacon.

These objects are reached according to the invention with a method fordetermining the correlation between on the one hand a signal transmittedby a beacon and received at a receiver tracking said beacon and on theother hand a reconstructed signal expected to be received at thereceiver from the beacon, wherein the received signal and thereconstructed signal are shifted against each other. The proposed methodcomprises as a first step multiplying a respective overlapping part ofthe received signal and the reconstructed signal for each shiftingposition. The multiplication can be performed in particular pointwisebetween the respective overlapping parts. The multiplications shouldtake into account a possible difference in the sampling rate in thereceived signal and the reconstructed signal, though.

The proposed method comprises as a second step dividing the overlappingpart for each shifting position into sections and integrating theproducts resulting in the preceding step within each section. It is tobe noted that the multiplications in the preceding step do notnecessarily have to be completed before these integrations start.Moreover, the division into sections can be performed already before themultiplication of the preceding step on the original samples of thereceived and on the reconstructed signal. It is only of relevance thatthe integration of the resulting products is performed separately foreach section.

In a third step of the proposed method, the result of the integration ofa respective first section is multiplied with a complex conjugatedversion of the result of the integration of a respective second section.The respective second section has a predetermined distance to therespective first section. This step is performed for a predeterminednumber of first sections, preferably for all sections as first sectionfor which there exists a second section at the predetermined distance.

The products resulting in the second multiplications are then integratedin a fourth step. Finally, at least the maximum value resulting in thefourth step for the different shifting positions is determined. Theshifting position with the maximum value is most probably the desiredshifting position with the maximum correlation.

It is to be noted that there may be small variations in the resultingcorrelation values, due to which the assumed shifting position with themaximum correlation may not be quite correct. It is therefore possible,for example, to determine not only the highest correlation value but afew of the highest correlation values, in case there are doubts that themaximum correlation results in a strong enough value in a certainsignal-to-noise condition. All of the associated positions can then betried in a desired further processing.

The objects of the invention are also reached with a receiver comprisingmeans for receiving and tracking signals from at least one beacon andprocessing means for realizing the proposed method.

The objects of the invention are further reached with a positioningsystem comprising a receiver and at least one network element of anetwork. This network may be a mobile communication network or any othernetwork. The receiver comprises again means for receiving and trackingsignals from at least one beacon and processing means for realizing thesteps of the proposed method. In addition, the receiver comprises meansfor communicating with the network.

Finally, the objects of the invention are reached according to theinvention with a positioning system, in which the steps of the proposedmethod are realized by a processing unit of the system which is externalto a receiver of the system. The receiver includes in this case meansfor receiving and tracking signals from at least one beacon and meansfor providing received and tracked beacon signals to the processingunit. The processing unit can also include other functions. It can begiven e.g. by a mobile station to which the receiver is connected andwhich is able to communicate with a mobile communication network forreceiving pieces of information. It can also be given by a networkelement of a network, in which required pieces of information areavailable.

The invention proceeds from the idea that the cross-correlationtechnique employed for time-recovery can be modified in a way that makesit immune to residual sinusoidal modulations. Ordinarycross-correlations perform for each shifting position a multiplicationof two signals followed by an integration. According to the invention,this integration is split up into two steps, between which a furtheroperation is inserted. First, the samples resulting in themultiplication are divided into sections, and only a partial integrationover the respective samples of each section is performed. The signalsresulting in the first integration step are further multiplied by acomplex conjugated and shifted version of itself. Only then, theresulting signals are integrated to obtain a single result for oneshifting position.

It is an advantage of the invention that the residual modulation in thesignals provided by a tracking loop of a receiver are compensated in thecross-correlation itself, which constitutes an alternative to the knownapproach. It is further an advantage of the invention that thesensitivity of the receiver is increased.

Preferred embodiments of the invention become apparent from thesubclaims.

In one preferred embodiment, the length of the sections for the partialintegrations is defined by the expected maximum possible frequency ofundesired sinusoidal modulations, e.g. a maximum possible Dopplerfrequency. In addition, the number of samples per bit in the receivedsignal should be taken into account when determining the length of thesections.

In a further preferred embodiment, the predetermined distance betweenthe respective first and second section is equally determined based onan expected maximum possible frequency of undesired sinusoidalmodulations present in the received signal. The determination can alsobe based on the determined length of the sections. The second sectioncan be the section next to the first section, but also be located at alarger distance of the first section.

Advantageously, the received signal is bit-synchronized before thecorrelation according to the invention is performed, since this enablesa correct alignment in each shifting position between the receivedsignal and the reconstructed signal.

The method according to the invention can be employed for computing theaccurate time when a received signal was transmitted by a beacon, sinceto the bits of the reconstructed signal, an identification may beassociated which enables to determine the time at which they would havebeen transmitted by the beacon.

The method according to the invention can further be employed forperforming a time initialization of the receiver time based on acomputed time of transmission.

For the time initialization, an accurate current time of the receiver atthe time of reception of the received signal can be determined as thesum of a determined accurate time of transmission and a time of flight.The time of flight can be determined based on an available position ofthe beacon at the accurate time of transmission of the received signaland on an available reference position of the receiver.

Alternatively, in case the receiver receives signals from at least fourbeacons and determines the accurate time of transmission of each ofthese signals, an accurate current time of the receiver at the time ofreception of the received signals can be determined by conventional GPSequations. It is possible to employ different methods for determiningthe time of transmission of signals in different channels. Thus, it isonly required that the time of transmission of the signal from one ofthe at least four beacons is determined according to the method of theinvention as basis for the GPS equations.

It is understood that the employed expression “accurate time” does notrefer to an absolute accuracy but only to a quite high accuracy.

In case the receiver is able to communicate with a network, the receivermay receive various information as a basis for the calculationsaccording to the invention. It is to be noted that the receiver can beable to communicate with the network either directly or indirectly, inthe case of a mobile communication network for instance via some mobilestation. A network may provide a receiver for example with a referencetime for the receiver, with a maximum error of this reference time, witha reference position of the receiver and with position information forat least one beacon. The position information can include in particularephemeris data and/or almanac data for at least one beacon. In somesituations, only ephemeris data, only almanac data or both might beavailable at a network, and only the available data can be provided. Asmentioned above, the network providing assistance data can be a mobilecommunication network, but it can also be any other kind of networkwhich is capable of providing assistance data via a network element,e.g. via a DGPS (Differential Global Positioning system) station.

In an advantageous embodiment of the positioning system according to theinvention including a network element of a network, the network elementcomprises therefore means for receiving and tracking signals from atleast one beacon, and moreover means for providing the receiver with atleast one of the above mentioned pieces of information. It is to benoted that in case pieces of information are provided by a network, notall of the listed pieces of information have to be provided. The maximumerror of a time reference could be specified for example by requirementsto the reference time in a standard or a system specification. In thiscase, there would be no necessity to communicate the maximum error tothe receiver, as it is known.

Each of the mentioned data may alternatively be stored in the receiveror be provided by some algorithm in the receiver or a connectedprocessing unit, e.g. another time-recovery algorithm providing anestimate of the current time and the maximum possible error in thisestimate. Thus, a receiver according to the invention can also operateindependently of assistance data from a network.

If some required information is missing at the processing means, asignal can only be partially reconstructed. But with some care, themethod according to the invention can still be applied. Notreconstructed bits could be replaced e.g. by 0, while reconstructed oneswill be set to ±1. A control can be maintained in the receiver duringeach cross-correlation by monitoring the number of “not reconstructed”bits having a value of “0”. If that number is not big, thecross-correlation is performed, but if the reconstructed array is foundto be almost empty, this fragment is not used and the receiver will waitfor a more favorable moment. Since different phases are compared bysliding and cross-correlating, the cross-correlation peak value dependson the number of “unknown” bits at the given stage, which number changesfrom one sliding position to the next. A kind of scaling may be used tonormalize properly, so that the method according to the invention stillworks normally with some unknown bits.

Preferably, though not necessarily, the modified cross-correlationaccording to the invention is implemented as software.

The invention can be employed in particular in the current GPS system,but equally in future extended GPS systems with new signals and in othersimilar beacon based positioning systems such as Galileo. It can furtherbe employed in any system in which a cross-correlation has to beperformed with beacon signals received at a receiver.

The beacon can be in particular, though not exclusively, a satellite ora base station of a mobile communication network.

Preferably, though not necessarily, the receiver is a GPS receiver andthe beacon is a GPS space vehicle.

BRIEF DESCRIPTION OF THE FIGURES

Other objects and features of the present invention will become apparentfrom the following detailed description of an exemplary embodiment ofthe invention considered in conjunction with the accompanying drawings,of which:

FIG. 1 illustrates the relation between the TOT of a received signal andthe preceding last bit edge received in the same channel;

FIG. 2 illustrates the correspondence between the error in an estimatedtime of transmission and the error in an estimated time of transmissionof the preceding last bit edge;

FIG. 3 is a flow chart illustrating a process of determining the currenttime in a GPS receiver;

FIG. 4 illustrates the determination of a bit reconstruction timeinterval for the process of FIG. 3;

FIG. 5 is a continuation of FIG. 4 and illustrates the cross-correlationof a raw data array with a reconstructed bit array; and

FIG. 6 illustrates in detail the cross-correlation of an embodiment ofthe method according to the invention employed in the process of FIG. 3.

DETAILED DESCRIPTION OF THE INVENTION

FIGS. 1 to 6 illustrate a process implemented in a GPS receiver forenabling a time-recovery of the GPS time based on a cross-correlationmodified according to the invention. The GPS receiver receives signalsfrom several GPS satellites and is able to track at least one of thesatellites by a tracking loop realized in a tracking unit of thereceiver by means of a correlator. Further, the GPS receiver comprisesthe functions of a mobile station and is thus able to receive additionalinformation from a base station of a mobile communication network towhich the receiver it is currently attached.

The time at which the last measurements were received by the GPSreceiver are referred to as current time, which current time is the timethat is to be determined as accurate GPS time in the proposedtime-recovery process.

First, some temporal relations existing for a satellite signal will bedescribed, on which temporal relations the proposed time-recovery isbased.

When the receiver tracks a satellite, it is able to count code epochs,each epoch comprising 1023 chips, as well as integer and fractionalchips. This is illustrated in FIG. 1 by means of a time bar. On thistime bar, the time of transmission of the last bit edge of a previouslyreceived signal is indicated. Further indicated on this time bar is thetime of transmission of a currently received signal. Whenever the termtime of transmission is used in the following without furtherspecification, it always relates to the time of transmission of such acurrently received signal. The time of transmission is calculated bysubtracting the time of flight TOF, which the signals require topropagate from the satellite to the receiver, from the time ofmeasurement, i.e from the current time. The time of transmission of thelast bit edge can be determined in an analogous same way.

A bit-synchronization algorithm applied by the tracking unit to atracked signal provides for the last bit edge a certain epoch counterreading. Moreover the algorithm provides the epoch/chip counter readingsfor the signal that was just received. Proceeding from the time oftransmission of the last bit edge, the receiver counts the epochs untilthe time of transmission of a newly received signal. In the example ofthe figure, 3 entire epochs are counted by the receiver between the timeof transmission of the last bit edge and the calculated time oftransmission of the current signal. The receiver moreover counts thechips between the last entire epoch and the calculated time oftransmission of the current signal. In the figure, there are 4 entirechips indicated between the third epoch and the time of transmission ofthe current signal. Finally, the receiver performs a fractional chipmeasurement, calculating the time between the last entire chip and thetime of transmission of the current signal. Since epochs and chips havea fixed duration at the satellite, the exact time duration from thetransmission of the last bit edge until the transmission of the receivedsignal can be determined based on the epoch and chip count.

As becomes apparent from FIG. 1, there is a one-to-one correspondencebetween the time of the last bit edge and the time when the new signalleft the satellite. This means that an error in the time estimate of thetime of transmission results in the same error in the estimate of thetime of transmission of the last bit edge. Estimating the time oftransmission of the last bit edge accurately would thus allow one torecover the accurate time of transmission of the new signal.

FIG. 2 illustrates by means of another time bar the timing uncertaintiesthat have to be dealt with when determining the accurate time oftransmission of the last bit edge.

At the right end of the time bar of FIG. 2, the true time oftransmission and an estimated time of transmission of a current signalare indicated. The estimated time of transmission is determined based onan estimate of the current time received from the network and on anassumed time of flight. Inaccuracies in the estimated time oftransmission thus result from errors in the estimate of the current timeand from errors in the TOF estimate. The true time of transmission liesin an interval given by the estimated time of transmission and a knownmaximum possible error extending in either direction of this estimatedtime of transmission. The maximum possible error depends on the qualityof the reference time. This interval is also indicated in the figure.

At the left end of the time bar of FIG. 2, the true time of transmissionof the last bit edge and an estimated time of transmission of the lastbit edge T_(lb) are indicated. The estimated time of transmission of thelast bit edge T_(lb) is determined based on the estimated time oftransmission of the current signal and on the epoch and chip counts fromthe last bit edge described with reference to FIG. 1. The time intervalbetween the time of transmission of the current signal and of the lastbit edge is indicated in the figure by a double headed arrow.

The estimated time of transmission of the last bit edge T_(lb) has thesame maximum possible error T_(err) in either direction as the estimatedtime of transmission of the current signal. The interval of the possiblemaximum error of the estimated time of transmission of the last bit edgeT_(lb) is equally depicted on the time bar, the interval being delimitedby a lower limit T_(lb−err) and a higher limit T_(lb+err), wherein(T_(lb−err), T_(lb+err))≡(T_(lb)−T_(err), T_(lb)+T_(err)). The true timeof transmission of the last bit edge lies within this interval, whichinterval may thus be considered as a search area for the true last bitedge.

The proposed process enabling a time-recovery of the GPS time is basedon these considerations and will now be described with reference to theblock diagram of FIG. 3, which shows the different steps of the process.The process is realized by a processing unit of the receiver with acorresponding software.

The processing unit receives from the base station, to which the GPSreceiver is currently attached, a reference position of the receiver, areference time, the maximum possible error of the reference time, andnavigation data from at least one satellite. Alternatively, suchinformation can be stored and/or generated within the receiver.

The GPS receiver is currently tracking at least this satellite, and thetracking unit provides in addition the raw data from the correspondingtracking channel to the processing unit. The term “raw data” means thatno determination on bit values was performed on the outputs of thecorrelator of the tracking unit on the base band tracking side. Theoutputs of the correlator comprise I (in-phase) and Q (quadrature)components, which are provided with some accuracy upon a request fromthe software of the processing unit.

As mentioned above, the tracking unit further applies abit-synchronization algorithm on the tracked signal. It is expected thata bit-synchronization is achieved in the channel of interest and thatthus the bit edges in the signal are known, even though the bitsthemselves are not easily identifiable due to noise. The bit edges areeasier to detect in weak signal conditions, since thebit-synchronization algorithm is an integration type of routine whichnarrows the noise bandwidth. Thus, the tracking unit can also provideepoch and chip counts to the processing unit.

In a first step of the process presented in FIG. 3, a time interval isdetermined which contains the correct GPS time of the transmission ofthe last received bit edge.

To this end, an estimate of the current time T_(curr) is determinedbased on the time reference received from the base station or from thelocal clock. The time uncertainty of the available time estimate, whichis equally received from the base station or known from systemspecifications, is denoted again with T_(err). For determining thedesired interval, moreover an estimate of the time of flight T_(TOF) isrequired, unless a nominal default value of 0.078 s is to be used. Thetime duration corresponding to consecutive raw samples accumulated up toa last bit edge of the received signal is referred to by T_(raw). Thetracking unit of the receiver measures the chip and epoch counts fromthe last bit edge as described with reference to FIG. 1 and providesthem to the processing unit. The entire time equivalent of the countedepochs, chips and fractional chip measurements from last bit edge to theestimated time of transmission of the received signal is denoted asT_(FromLastBit). The time of transmission of the last bit edge from thesatellite is then expected to lie in the interval:(T_(lb − err), T_(lb + err)) ≡ (T_(curr) − T_(TOF) − T_(FromLastBit) − T_(err), T_(curr) − T_(TOF) − T_(FromLastBit) + T_(err))

In a second step, which is also indicated in FIG. 3, the time oftransmission of the last received bit edge is estimated more precisely.This further estimation is based on cross-correlating the received rawdata array with a reconstructed bit array. The determination of the bitreconstruction interval required to this end is illustrated in FIG. 4.

FIG. 4 shows another time bar. As in FIG. 2, the estimated time oftransmission of the last bit edge T_(lb), the true time of transmissionof the last bit edge, and the boundaries T_(lb−err), T_(lb−err) for themaximum possible error in the estimated time of transmission of the lastbit edge T_(lb) are depicted. A first horizontal beam a) furtherillustrates that the true time position of the received raw data withthe duration T_(raw) ends exactly with the true time of transmission ofthe last bit edge, when the raw data is shifted back in time accordingto the known regularities of the GPS signal. A second horizontal beam b)illustrates the earliest possible position of the raw data array and athird horizontal beam c) the latest possible position of the raw dataarray, when assuming that the unknown last bit edge time lies within theabove defined interval (T_(lb−err), T_(lb+err)).

When determining the bit reconstruction interval for which bits have tobe reconstructed from available navigation data for thecross-correlation, it has to be ensured that reconstructed bits areavailable for correlations with the raw data proceeding from thedepicted earliest possible position to the depicted latest possibleposition. This means that reconstructed bits have to be providedbeginning at a time of the duration T_(raw) of the raw data before theearliest possible bit edge time T_(lb−err), and ending with the latestpossible last bit edge time T_(lb+err).

The bit reconstruction interval, which is shown as fourth horizontalbeam d) in FIG. 4, can thus be calculated to:

(T_(start), T_(end))≡(T_(lb−err)−T_(raw), T_(lb+err)).

In a next step, a navigation data reconstruction routine of aframe-reconstructor of the processing unit is called. The routinereconstructs the navigation data bits using the satellite parametersreceived from the network. The navigation bits are reconstructed for theentire determined time interval (T_(start), T_(end)). Each bit in thereconstructed array of bits can be identified by its address in thenavigation message, i.e. by the frame number, by the subframe number andby the bit index in that subframe.

FIG. 5 is a continuation of FIG. 4 and shows again the true time oftransmission of the last bit edge, the estimated time of transmission ofthe last bit edge T_(lb), the limits for the maximal possible error ofthe estimated time T_(lb−err) and T_(lb+err), a horizontal beam b)indicating the earliest possible position of the raw data array and ahorizontal beam d) representing the bit reconstruction interval. Inaddition, the reconstructed bit array is depicted in FIG. 5 ashorizontal beam f).

In a third step of the process illustrated by the flow chart of FIG. 3,a cross-correlation is performed between the raw data array, representedin FIG. 5 by a horizontal beam e), and the reconstructed bit array ofbeam f), in order to find the best match between the raw data and aspecific fragment of the reconstructed bit array.

The accumulated data in the raw data array of beam e) is compared todifferent fragments of the reconstructed bit array of beam f), whichfragments have the same duration T_(raw) as the raw data array, byshifting the raw data array along the reconstructed bit array andcross-correlating overlapping sections at each shifting position. Theresults of the cross-correlations at each shifting position arecollected in an array. A diagram g) presenting an exemplary distributionof the values in such an array is shown in FIG. 5, the values beingassociated to the last bit in the respective fragment of thereconstructed bit array employed in a correlation on the time bar. Fromthis array, the maximum absolute value is selected and the correspondingshifting position determined. The fragment of the reconstructed dataarray associated to this shifting position is expected to constitute thebest match for the raw data array. In FIG. 5, the diagram showsaccordingly a clear maximum at the true time of transmission of the lastbit edge.

The last received bit of the raw data array can thus be associated tothe last bit in the determined fragment of the reconstructed array.Since the bit addresses of all reconstructed bits in the reconstructioninterval are known, also the last bit of the determined fragment can beclearly identified. The identification of the last bit in asubframe/bit-in-subframe format allows finding of the exact GPS time ofthe transmission of the last bit edge.

In a further step of the process of FIG. 3, the time when the receivedsignal left the satellite is computed as accurate time of transmissionT_(TOT). The reconstructed bit addresses are known with the knownSubframeNumber and LastBitNumber, which enable to determine a firstcomponent of the accurate time of transmission. The processing unitfurther received from the tracking unit the epoch count at the estimatedlast bit edge LastBitEpochCount as well as the current epoch countCurrentEpochCount, i.e. the epoch count at the time of reception of thereceived signal, and equally sub-millisecond chip count measurements inseconds, which is denoted as C/A and enables the determination of asecond component of the accurate time of transmission. The entireaccurate time of transmission T_(TOT) can be computed as:$\begin{matrix}{T_{TOT} = {{{SubframeNumber}*6s} +}} \\{{{{LastBitNumber}*20\quad {ms}} +}} \\{{{\left( {{CurrentEpochCount} - {LastBitEpochCount}} \right)*1\quad {ms}} +}} \\{\left( {{IntegerChipCountInSeconds} +} \right.} \\\left. {FractionalChipCountInSeconds} \right)\end{matrix}$

In a last step of the process of FIG. 3, the current time estimate isrefined at the receiver.

The way in which this refinement takes place depends on whether theaccurate time of transmission can be determined for signals of at leastfour or of less than four satellites.

In case signals from less than four satellites are received, theposition of one satellite is calculated from the accurate time oftransmission determined for this satellite and from ephemeris datareceived from the base station for this satellite. Then, the time offlight is calculated based on the reference position of the userprovided by the base station and on the determined position of thesatellite. The current time is estimated as the sum of the accurate timeof transmission and the determined time of flight.

In case the accurate time of transmission is available for at least 4satellites, also ordinary GPS position and time calculation methods canbe used, e.g. a Least Squares method.

FIG. 6 illustrates in more detail the correlation technique employed inthe above described method for overcoming the problems resulting from aresidual sinusoidal modulation in the raw data provided to theprocessing unit of the receiver, in particular a Doppler frequency.

In a first row a) of FIG. 6, an array with reconstructed bits isdepicted. The array corresponds to the array represented in FIG. 5 bybeam f). The replica is sampled with one sample per bit in the currentexample, each bit being represented in the array by a black circle.

In a second row b), an array of raw data from a tracking channel isshown. The raw data has a known number of samples per bit, each bitbeing represented in the array by a black circle. This array correspondsto the array represented in FIG. 5 by beam e). The satellite signal hastwo components I and Q, and each raw data sample is interpreted as acomplex number with I and Q representing the real and imaginary partsappropriately.

The raw data array of row b) slides along the reconstructed signal ofrow a), and the processing unit tries to find a similar bit pattern inthe replica. In the current sliding position, the array of raw data isaligned with a fragment of the reconstructed signal which is delimitedin row a) by two vertical lines.

Instead of performing a cross-correlation directly on the respective twosets of data, a modified algorithm is applied, as illustrated in rows c)to h) of FIG. 6. As input for this algorithm, the array of row b)containing the raw received signal (X_(s)(n)) and an array containing afragment of the reconstructed signal (X_(r)(n)) of row a) for arespective sliding position are provided. Further, the lengths of botharrays (N_(s), N_(r)), the possible range of sinusoidal modulationfrequencies remaining after the tracking (ΔF), and the number of samplesper bit (k_(s/b)) in the received signal are provided.

In a first step, the algorithm splits the array with the fragment of thereconstructed signal and the array with the raw data into sections ofequal size, as illustrated in row c) and d), respectively. The length ofthe sections (N_(ss)) is calculated from the maximal possible Dopplerfrequency ΔF. The length can be calculated for example by the equation:$\begin{matrix}{{N_{ss} = {{floor}\left( \frac{1000.0 \cdot k_{s/b}}{20\quad \Delta \quad F} \right)}};} \\{{{{{if}\left( {N_{ss} = 0} \right)}{then}\quad N_{ss}} = 1};}\end{matrix}$

if the input to the algorithm is taken from the output of the trackingchannel correlator. The function floor ( . . . ) has as an output theclosest integer not exceeding the value of the argument. In case thelength N_(ss) of the sections results in zero in this equation, thelength is set to N_(ss)=1.

The correlation for each alignment position l is now computed by thealgorithm based on two equations realizing four steps.

The first equation is used for determining the correlationR_(section)(l, k_(s)) for each section k_(s) at a specific alignmentposition l, the number of sections being denoted as K_(s):$\begin{matrix}{{{R_{section}\left( {l,k_{s}} \right)} = {\sum\limits_{n_{ss} = 0}^{N_{ss} - 1}\quad {{X_{r}\left( {l + \left\lfloor {\left( {n_{ss} + {k_{s}N_{ss}}} \right)/k_{s/b}} \right\rfloor} \right)}{X_{s}\left( {n_{ss} + {k_{s}N_{ss}}} \right)}}}},} \\{{{l = 0},1,\ldots \quad,{N - \left\lfloor {K_{s}{N_{ss}/k_{s/b}}} \right\rfloor},\quad {k_{s} = 0},1,\ldots \quad,{K_{s} - 1}}\quad}\end{matrix}$

The first equation thus performs a step of a pointwise multiplication ofthe samples of the reconstructed signal and the raw data in eachsection, realized in the equation by the multiplication of X_(r) andX_(s). The equation further comprises the step of a coherentintegration, realized in the equation by the summing element Σ.

The results of the subcorrelations, which are represented in FIG. 6 inrow f), are then combined in row g) in a way compensating or removingthe remaining sinusoidal modulation.

To this end, the second equation is used for determining the finalcorrelation R²(l) at a specific alignment position l as: $\begin{matrix}{{{R^{2}(l)} = {\sum\limits_{k_{s} = 0}^{K_{s} - 1 - k_{shift}}\quad {{R_{section}\left( {l,k_{s}} \right)}{R_{section}^{*}\left( {l,{k_{s} + k_{shift}}} \right)}}}},} \\{where} \\{k_{shift} = \left\{ \begin{matrix}{1,{N_{ss} \geq k_{s/b}}} \\{{{ceil}\left( \frac{k_{s/b}}{N_{ss}} \right)},{N_{ss} < k_{s/b}}}\end{matrix} \right.}\end{matrix}$

The function ceil ( . . . ) has as an output the closest integerexceeding the value of the argument.

The second equation thus performs a step of multiplying thesubcorrelations with a conjugated version shifted by k_(shift) in time,which is realized in the equation by the multiplication of R_(section)and R*_(section). The second equation further performs the final step ofa non-coherent integration, realized in the equation by the summingelement Σ.

The resulting value for the final correlation for the current alignmentposition is put to a corresponding position in an array, as indicated inrow h) of FIG. 6. This array corresponds to the diagram g) in FIG. 5.

When the final correlation value for all alignment positions isprovided, the maximum value is determined by the algorithm, as indicatedin row i) of FIG. 6.

Finally, the phase of the alignment position corresponding to thismaximum correlation value is determined, as indicated in row j) of FIG.6, in order to compute the time of transmission of the signal resultingin the raw data, as described above with reference to FIG. 3.

What is claimed is:
 1. A method for determining the correlation betweenon the one hand a signal transmitted by a beacon and received at areceiver tracking said beacon and on the other hand a reconstructedsignal expected to be received at said receiver from said beacon,wherein said received signal and said reconstructed signal are shiftedagainst each other, said method comprising: a) multiplying a respectiveoverlapping part of said received signal and said reconstructed signalfor each shifting position; b) dividing the overlapping part for eachshifting position into sections and integrating the products resultingin the preceding step within each section; c) multiplying the result ofthe integration of a respective first section with a complex conjugatedversion of the result of the integration of a respective second sectionhaving a predetermined distance to the first section for a predeterminednumber of first sections; d) integrating the products resulting in stepc); and e) determining at least the maximum value resulting in step d)for the different shifting positions, the shifting position with themaximum value being the most probable candidate of being the shiftingposition with the maximum correlation.
 2. A method according to claim 1,wherein the length of said sections is determined based on a maximumpossible frequency of undesired sinusoidal modulations present in saidreceived signal.
 3. A method according to claim 2, wherein the length ofsaid sections is determined in addition based on the number of samplesper bit in said received signal.
 4. A method according to claim 1,wherein said predetermined distance between said respective first andsecond section is determined based on a maximum possible frequency ofundesired sinusoidal modulations present in said received signal.
 5. Amethod according to claim 1, comprising in the multiplications of stepa) taking into account a possible difference in the sampling rate insaid received signal and said reconstructed signal.
 6. A methodaccording to claim 1, wherein a bit-synchronization is achieved for saidreceived signal before performing said steps a) to d).
 7. A methodaccording to claim 1, wherein said reconstructed beacon signal isconstructed by: computing a time interval (T_(start), T_(end))containing the time of the transmission of a last bit edge preceding thetransmission of said received beacon signal in the channel of saidreceived beacon signal as (T_(start),T_(end))=(T_(curr)−T_(TOF)−T_(FromLastBit)−T_(err)−T_(raw),T_(curr)−T_(TOF)−T_(FromLastBit)+T_(err)), wherein T_(curr) is anestimated time of arrival of said received beacon signal, whereinT_(TOF) is an estimated time of flight of said received beacon signal,wherein T_(FromLastBit) is a determined time between an estimated timeof transmission of said last bit edge and an estimated time oftransmission of said received beacon signal, wherein T_(err) is a totaltime uncertainty of the available time estimates T_(curr) and T_(TOF),and wherein T_(raw) is the length of the received beacon signal; andreconstructing said reconstructed beacon signal for said determined timeinterval (T_(start), T_(end)).
 8. A method according to claim 1, whereinstep e) is followed by computing the accurate time when said receivedsignal was transmitted by said beacon, which accurate time oftransmission of said received beacon signal is computed based on a bitaddress associated with the last bit of a fragment of said reconstructedbeacon signal presenting the highest correlation value in saidcross-correlation with said received beacon signal, and on the timedifference between the transmission of said last bit edge and thetransmission of said received beacon signal, which time difference isdetermined based on epoch, chip and fractional chip measurements on thechannel on which said received beacon signal is received.
 9. A methodaccording to claim 1, wherein step e) is followed by computing theaccurate time when said received signal was transmitted by said beacon,and by performing a time initialization of the receiver time based onsaid time of transmission.
 10. A method according to claim 9, whereinfor said time initialization, an accurate current time of said receiverat the time of reception of said received signal is determined as thesum of a determined accurate time of transmission and a time of flight,which time of flight is determined based on an available position ofsaid beacon at the accurate time of transmission of said received signaland on an available reference position of said receiver.
 11. A methodaccording to claim 9, wherein said receiver receives signals from atleast four beacons, wherein said time initialization comprisesdetermining an accurate current time of said receiver at the time ofreception of at least one of said received signals based on GPSequations utilizing the accurate time of transmission of signals fromsaid at least four beacons, wherein the accurate time of transmission ofa signal from at least one of said beacons is determined according toclaim
 9. 12. A method according to claim 1, wherein a network providesat least one of the following pieces of information: a reference timefor the receiver, a maximum error of a reference time, a referenceposition of the receiver and position information for at least onebeacon.
 13. A method according to claim 1, wherein said beacon is asatellite.
 14. A method according to claim 13, wherein said receiver isa GPS receiver and wherein said satellite is a GPS space vehicle.
 15. Amethod according to claim 1, wherein said beacon is a base station of acommunication network.
 16. A receiver comprising means for receiving andtracking signals from at least one beacon and processing means forrealizing the steps of the method according to claim
 1. 17. Apositioning system comprising a receiver and at least one networkelement of a network, said receiver including means for communicatingwith said network, receiving means for receiving and tracking signalsfrom at least one beacon and processing means for realizing the steps ofthe method according to claim
 1. 18. A positioning system according toclaim 17, wherein said network element includes receiving means forreceiving and tracking signals from said at least one beacon and meansfor providing said receiver with at least one of the followinginformation: a reference time for said receiver, a maximum error of areference time, a reference position of said receiver and positioninformation for said beacon.
 19. A positioning system according to claim17, wherein said network is a mobile communication network.
 20. Apositioning system comprising a receiver and a processing unit externalto said receiver, said receiver including receiving means for receivingand tracking signals from at least one beacon and means for providingreceived and tracked beacon signals to said processing unit, and saidprocessing unit comprising means for realizing the steps of the methodaccording to claim
 1. 21. A positioning system according to claim 20,further comprising at least one network element of a network, whereinsaid processing unit comprises means for communicating with said networkelement, and wherein said network element includes receiving means forreceiving and tracking signals from said beacon and means for providingsaid processing unit with at least one of the following pieces ofinformation: a reference time for said receiver, a maximum error of areference time, a reference position of said receiver and positioninformation for said beacon.
 22. A positioning system according to claim21, wherein said network is a mobile communication network.